Bearings | Mathematics for GCSE/IGCSE - Year 11 PDF Download

What are bearings?

• Bearings describe and use directions in terms of angles.
• They are precisely defined for navigation purposes to provide exact locations and directions.

How are bearings defined?

• There are three rules to follow when defining a bearing:
  • Bearings are measured from the North direction, typically shown as straight up on a scale drawing or map.
• Bearings are measured clockwise from North. If confused, refer to a wall clock for guidance.
• Bearings should always be written with three digits, so angles under 100° should have leading zeros (e.g., 059, 008).
• Note that degree symbols are generally not used when referring to bearings.

What are bearings used for?

• Bearings questions typically involve using Pythagoras' theorem or trigonometry to determine missing distances (lengths) and directions (angles) in navigation problems.
• Always draw a diagram for clarity.
• You may be given a scale or need to consider using one.
• Some questions might require using angle facts to find the missing directions.
• To solve a bearings question, follow these steps:
  • Step 1: Draw a diagram, including any points and distances provided.
  • Step 2: Draw a North line (an arrow pointing straight up) at the point from which you are measuring the bearing. If the bearing from A to B is given, draw the North line at point A.
  • Step 3: Measure the given bearing angle clockwise from the North line.
  • Step 4: Draw a line and mark point B at the specified distance.
• Use Pythagoras' theorem or trigonometry to calculate any additional distances needed.

How are bearings used on maps?

• If you find yourself needing to determine a direction on a map, here is a step-by-step guide using a protractor:
  • Always start by drawing the North line on your map.
  • Measure the angle clockwise from the North direction.
  • Express the angle using three figures for accuracy.
• Understanding the cardinal compass directions can be beneficial. Here are some key bearings and how to represent them:
  • Due east corresponds to a bearing of 090°. Draw the line directly to the right.
  • Due south corresponds to a bearing of 180°. Draw the line vertically downwards.
  • Due west corresponds to a bearing of 270°. Draw the line directly to the left.
  • Due north corresponds to a bearing of 360° (or 000°). Draw the line vertically upwards.
• For directions that fall in between these cardinal points, you can use combinations. Here are some examples:
  • Due Northeast falls on a bearing of 045°, halfway between North (000°) and East (090°).
  • Due Southeast falls on a bearing of 135°.
  • Due Southwest falls on a bearing of 225°.
  • Due Northwest falls on a bearing of 315°.
• Using the above bearings for compass directions will help you to estimate angles for other bearings on the map